Abstract
Real count data time series often show an excessive number of zeros, which can form quite different patterns. We develop four extensions of the binomial autoregressive model for autocorrelated counts with a bounded support, which can accommodate a broad variety of zero patterns. The stochastic properties of these models are derived, and ways of parameter estimation and model identification are discussed. The usefulness of the models is illustrated, among others, by an application to the monetary policy decisions of the National Bank of Poland.
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References
Barreto-Souza W (2015) Zero-modified geometric INAR(1) process for modelling count time series with deflation or inflation of zeros. J Time Ser Anal 36(6):839–852
Billingsley P (1961) Statistical inference for Markov processes. Statistical research monographs, University of Chicago Press
Emiliano PC, Vivanco MJF, De Menezes FS (2014) Information criteria: how do they behave in different models? Comput Stat Data Anal 69:141–153
Fox AJ (1972) Outliers in time series. J R Stat Soc B 34(3):350–363
Gonçalves E, Mendes-Lopes N, Silva F (2016) Zero-inflated compound Poisson distributions in integer-valued GARCH models. Statistics 50(3):558–578
Grunwald G, Hyndman RJ, Tedesco L, Tweedie RL (2000) Non-Gaussian conditional linear AR(1) models. Aust N Z J Stat 42(4):479–495
Hilbe JM (2014) Modeling count data. Cambridge University Press, New York
Jazi MA, Jones G, Lai C-D (2012) First-order integer valued processes with zero inflated Poisson innovations. J Time Ser Anal 33(6):954–963
Jung RC, Kukuk M, Liesenfeld R (2006) Time series of count data: modelling and estimation and diagnostics. Comput Stat Data Anal 51(4):2350–2364
McKenzie E (1985) Some simple models for discrete variate time series. Water Resour Bull 21(4):645–650
Möller TA, Silva ME, Weiß CH, Scotto MG, Pereira I (2016) Self-exciting threshold binomial autoregressive processes. AStA Adv Stat Anal 100(4):369–400
Nastić AS, Ristić MM, Miletić Ilić A (2017) A geometric time series model with an alternative dependent Bernoulli counting series. Commun Stat Theory Methods 46(2):770–785
Rubin DB (1976) Inference and missing data. Biometrika 63(3):581–592
Seneta E (1983) Non-negative matrices and Markov chains, 2nd edn. Springer Verlag, New York
Sirchenko A (2013) A model for ordinal responses with an application to policy interest rate. NBP Working paper No 148
Steutel FW, van Harn K (1979) Discrete analogues of self-decomposability and stability. Ann Probab 7(5):893–899
Weiß CH (2009a) Monitoring correlated processes with binomial marginals. J Appl Stat 36(4):399–414
Weiß CH (2009b) A new class of autoregressive models for time series of binomial counts. Commun Stat Theory Methods 38(4):447–460
Weiß CH, Homburg A, Puig P (2016) Testing for zero inflation and overdispersion in INAR(1) models. Statistical Papers, to appear
Weiß CH, Kim H-Y (2013) Binomial AR (1) processes: moments, cumulants, and estimation. Statistics 47(3):494–510
Weiß CH, Kim H-Y (2014) Diagnosing and modeling extra-binomial variation for time-dependent counts. Appl Stochast Models Bus Ind 30(5):588–608
Weiß CH, Pollett PK (2012) Chain binomial models and binomial autoregressive processes. Biometrics 68(3):815–824
Weiß CH, Pollett PK (2014) Binomial autoregressive processes with density dependent thinning. J Time Ser Anal 35(2):115–132
Weiß CH, Testik MC (2015) On the Phase I analysis for monitoring time-dependent count processes. IIE Trans 47(3):294–306
Zeileis A, Kleiber C, Jackman S (2008) Regression models for count data in R. J Stat Softw 27(8):1–25
Zhu F (2012) Zero-inflated Poisson and negative binomial integer-valued GARCH models. J Stat Plann Infer 142(4):826–839
Zucchini W, MacDonald IL (2009) Hidden markov models for time series: an introduction using R. Chapman and Hall/CRC, London
Zuur AF, Ieno EN, Walker NJ, Saveliev AA, Smith GM (2009) Mixed effects models and extensions in ecology with R. Springer, New York
Acknowledgements
The authors thank the referee for carefully reading the article and for the comments, which greatly improved the article. H.-Y. Kim’s study is supported by the project “Small & Medium Business Administration” under Project S2312692 “Technological Innovation Development Business” for the innovative company in the year 2015. Main parts of this research were completed while H.-Y. Kim stayed as a guest professor at the Helmut Schmidt University in Hamburg.
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Möller, T.A., H. Weiß, C., Kim, HY. et al. Modeling Zero Inflation in Count Data Time Series with Bounded Support. Methodol Comput Appl Probab 20, 589–609 (2018). https://doi.org/10.1007/s11009-017-9577-0
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DOI: https://doi.org/10.1007/s11009-017-9577-0